Multilevel Decoders Surpassing Belief Propagation on the Binary Symmetric Channel

TL;DR

This paper introduces a new class of quantized message-passing decoders for LDPC codes over the BSC that outperform traditional belief propagation and min-sum algorithms by leveraging trapping set knowledge, even with limited message levels.

Contribution

The paper presents a novel decoding approach that uses trapping set insights to design efficient decoders surpassing BP and min-sum performance with lower complexity.

Findings

3-bit decoders outperform BP and min-sum

Decoders correct more errors than traditional algorithms

Significant complexity reduction achieved

Abstract

In this paper, we propose a new class of quantized message-passing decoders for LDPC codes over the BSC. The messages take values (or levels) from a finite set. The update rules do not mimic belief propagation but instead are derived using the knowledge of trapping sets. We show that the update rules can be derived to correct certain error patterns that are uncorrectable by algorithms such as BP and min-sum. In some cases even with a small message set, these decoders can guarantee correction of a higher number of errors than BP and min-sum. We provide particularly good 3-bit decoders for 3-left-regular LDPC codes. They significantly outperform the BP and min-sum decoders, but more importantly, they achieve this at only a fraction of the complexity of the BP and min-sum decoders.